Characterizing Sensor Performance (2):

Characterizing Sensor Performance (2) Basic sensor response ratings (cont.)
Resolution
minimum difference between two values
usually: lower limit of dynamic range = resolution
for digital sensors it is usually the A/D resolution.
e.g. 5V / 255 (8 bit)
Linearity
variation of output signal as function of the input signal
linearity is less important when signal is after treated with a computer
Bandwidth or Frequency
the speed with which a sensor can provide a stream of readings
usually there is an upper limit depending on the sensor and the sampling rate
Lower limit is also possible, e.g. acceleration sensor 4.1.2

In Situ Sensor Performance (1):

In Situ Sensor Performance (1) Characteristics that are especially relevant for real world environments
Sensitivity
ratio of output change to input change
however, in real world environment, the sensor has very often high sensitivity to other environmental changes, e.g. illumination
Cross-sensitivity
sensitivity to environmental parameters that are orthogonal to the target parameters
Error / Accuracy
difference between the sensor’s output and the true value
m = measured value
v = true value 4.1.2

In Situ Sensor Performance (2):

In Situ Sensor Performance (2) Characteristics that are especially relevant for real world environments
Systematic error -> deterministic errors
caused by factors that can (in theory) be modeled -> prediction
e.g. calibration of a laser sensor or of the distortion cause by the optic of a camera
Random error -> non-deterministic
no prediction possible
however, they can be described probabilistically
e.g. Hue instability of camera, black level noise of camera ..
Precision
reproducibility of sensor results 4.1.2

Characterizing Error: The Challenges in Mobile Robotics:

Characterizing Error: The Challenges in Mobile Robotics Mobile Robot has to perceive, analyze and interpret the state of the surrounding
Measurements in real world environment are dynamically changing and error prone.
Examples:
changing illuminations
specular reflections
light or sound absorbing surfaces
cross-sensitivity of robot sensor to robot pose and robot-environment dynamics
rarely possible to model -> appear as random errors
systematic errors and random errors might be well defined in controlled environment. This is not the case for mobile robots !! 4.1.2

Multi-Modal Error Distributions: The Challenges in …:

Multi-Modal Error Distributions: The Challenges in … Behavior of sensors modeled by probability distribution (random errors)
usually very little knowledge about the causes of random errors
often probability distribution is assumed to be symmetric or even Gaussian
however, it is important to realize how wrong this can be!
Examples:
Sonar (ultrasonic) sensor might overestimate the distance in real environment and is therefore not symmetric
Thus the sonar sensor might be best modeled by two modes: - mode for the case that the signal returns directly - mode for the case that the signals returns after multi-path reflections.
Stereo vision system might correlate to images incorrectly, thus causing results that make no sense at all
4.1.2

Wheel / Motor Encoders (1):

Wheel / Motor Encoders (1) measure position or speed of the wheels or steering
wheel movements can be integrated to get an estimate of the robots position -> odometry
optical encoders are proprioceptive sensors
thus the position estimation in relation to a fixed reference frame is only valuable for short movements.
typical resolutions: 2000 increments per revolution.
for high resolution: interpolation 4.1.3

Wheel / Motor Encoders (2):

Wheel / Motor Encoders (2) 4.1.3

Heading Sensors:

Heading Sensors
Heading sensors can be proprioceptive (gyroscope, inclinometer) or exteroceptive (compass).
Used to determine the robots orientation and inclination.
Allow, together with an appropriate velocity information, to integrate the movement to an position estimate.
This procedure is called dead reckoning (ship navigation) 4.1.4

Compass:

Compass Since over 2000 B.C.
when Chinese suspended a piece of naturally magnetite from a silk thread and used it to guide a chariot over land.
Magnetic field on earth
absolute measure for orientation.
Large variety of solutions to measure the earth magnetic field
mechanical magnetic compass
direct measure of the magnetic field (Hall-effect, magnetoresistive sensors)
Major drawback
weakness of the earth field
easily disturbed by magnetic objects or other sources
not feasible for indoor environments 4.1.4

Gyroscope:

Gyroscope Heading sensors, that keep the orientation to a fixed frame
absolute measure for the heading of a mobile system.
Two categories, the mechanical and the optical gyroscopes
Mechanical Gyroscopes
Standard gyro
Rated gyro
Optical Gyroscopes
Rated gyro 4.1.4

Mechanical Gyroscopes:

Mechanical Gyroscopes Concept: inertial properties of a fast spinning rotor
gyroscopic precession
Angular momentum associated with a spinning wheel keeps the axis of the gyroscope inertially stable.
Reactive torque t (tracking stability) is proportional to the spinning speed w, the precession speed W and the wheels inertia I.
No torque can be transmitted from the outer pivot to the wheel axis
spinning axis will therefore be space-stable
Quality: 0.1° in 6 hours
If the spinning axis is aligned with the north-south meridian, the earth’s rotation has no effect on the gyro’s horizontal axis
If it points east-west, the horizontal axis reads the earth rotation 4.1.4

Rate gyros:

Rate gyros Same basic arrangement shown as regular mechanical gyros
But: gimble(s) are restrained by a torsional spring
enables to measure angular speeds instead of the orientation.
Others, more simple gyroscopes, use Coriolis forces to measure changes in heading. 4.1.4

Optical Gyroscopes:

Optical Gyroscopes First commercial use started only in the early 1980 when they where first installed in airplanes.
Optical gyroscopes
angular speed (heading) sensors using two monochromic light (or laser) beams from the same source.
On is traveling in a fiber clockwise, the other counterclockwise around a cylinder
Laser beam traveling in direction of rotation
slightly shorter path -> shows a higher frequency
difference in frequency Df of the two beams is proportional to the angular velocity W of the cylinder
New solid-state optical gyroscopes based on the same principle are build using microfabrication technology. 4.1.4

Ground-Based Active and Passive Beacons:

Ground-Based Active and Passive Beacons Elegant way to solve the localization problem in mobile robotics
Beacons are signaling guiding devices with a precisely known position
Beacon base navigation is used since the humans started to travel
Natural beacons (landmarks) like stars, mountains or the sun
Artificial beacons like lighthouses
The recently introduced Global Positioning System (GPS) revolutionized modern navigation technology
Already one of the key sensors for outdoor mobile robotics
For indoor robots GPS is not applicable,
Major drawback with the use of beacons in indoor:
Beacons require changes in the environment -> costly.
Limit flexibility and adaptability to changing environments. 4.1.5

Global Positioning System (GPS) (1):

Global Positioning System (GPS) (1) Developed for military use
Recently it became accessible for commercial applications
24 satellites (including three spares) orbiting the earth every 12 hours at a height of 20.190 km.
Four satellites are located in each of six planes inclined 55 degrees with respect to the plane of the earth’s equators
Location of any GPS receiver is determined through a time of flight measurement
Technical challenges:
Time synchronization between the individual satellites and the GPS receiver
Real time update of the exact location of the satellites
Precise measurement of the time of flight
Interferences with other signals 4.1.5

Global Positioning System (GPS) (2):

Global Positioning System (GPS) (2) 4.1.5

Global Positioning System (GPS) (3):

Global Positioning System (GPS) (3) Time synchronization:
atomic clocks on each satellite
monitoring them from different ground stations.
Ultra-precision time synchronization is extremely important
electromagnetic radiation propagates at light speed,
Roughly 0.3 m per nanosecond.
position accuracy proportional to precision of time measurement.
Real time update of the exact location of the satellites:
monitoring the satellites from a number of widely distributed ground stations
master station analyses all the measurements and transmits the actual position to each of the satellites
Exact measurement of the time of flight
the receiver correlates a pseudocode with the same code coming from the satellite
The delay time for best correlation represents the time of flight.
quartz clock on the GPS receivers are not very precise
the range measurement with four satellite
allows to identify the three values (x, y, z) for the position and the clock correction ΔT
Recent commercial GPS receiver devices allows position accuracies down to a couple meters. 4.1.5